MAYBE 719.35/297.04 MAYBE 719.35/297.04 719.35/297.04 We are left with following problem, upon which TcT provides the 719.35/297.04 certificate MAYBE. 719.35/297.04 719.35/297.04 Strict Trs: 719.35/297.04 { app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y) 719.35/297.04 , helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 719.35/297.04 , plus(x, 0()) -> x 719.35/297.04 , plus(x, s(y)) -> s(plus(x, y)) 719.35/297.04 , length(nil()) -> 0() 719.35/297.04 , length(cons(x, y)) -> s(length(y)) 719.35/297.04 , if(true(), c, l, ys, zs) -> nil() 719.35/297.04 , if(false(), c, l, ys, zs) -> 719.35/297.04 helpb(c, l, greater(ys, zs), smaller(ys, zs)) 719.35/297.04 , ge(x, 0()) -> true() 719.35/297.04 , ge(0(), s(x)) -> false() 719.35/297.04 , ge(s(x), s(y)) -> ge(x, y) 719.35/297.04 , helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 719.35/297.04 , greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 719.35/297.04 , smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 719.35/297.04 , helpc(true(), ys, zs) -> ys 719.35/297.04 , helpc(false(), ys, zs) -> zs } 719.35/297.04 Obligation: 719.35/297.04 runtime complexity 719.35/297.04 Answer: 719.35/297.04 MAYBE 719.35/297.04 719.35/297.04 None of the processors succeeded. 719.35/297.04 719.35/297.04 Details of failed attempt(s): 719.35/297.04 ----------------------------- 719.35/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 719.35/297.04 following reason: 719.35/297.04 719.35/297.04 Computation stopped due to timeout after 297.0 seconds. 719.35/297.04 719.35/297.04 2) 'Best' failed due to the following reason: 719.35/297.04 719.35/297.04 None of the processors succeeded. 719.35/297.04 719.35/297.04 Details of failed attempt(s): 719.35/297.04 ----------------------------- 719.35/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 719.35/297.04 seconds)' failed due to the following reason: 719.35/297.04 719.35/297.04 Computation stopped due to timeout after 148.0 seconds. 719.35/297.04 719.35/297.04 2) 'Best' failed due to the following reason: 719.35/297.04 719.35/297.04 None of the processors succeeded. 719.35/297.04 719.35/297.04 Details of failed attempt(s): 719.35/297.04 ----------------------------- 719.35/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 719.35/297.04 following reason: 719.35/297.04 719.35/297.04 The processor is inapplicable, reason: 719.35/297.04 Processor only applicable for innermost runtime complexity analysis 719.35/297.04 719.35/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 719.35/297.04 to the following reason: 719.35/297.04 719.35/297.04 The processor is inapplicable, reason: 719.35/297.04 Processor only applicable for innermost runtime complexity analysis 719.35/297.04 719.35/297.04 719.35/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 719.35/297.04 failed due to the following reason: 719.35/297.04 719.35/297.04 None of the processors succeeded. 719.35/297.04 719.35/297.04 Details of failed attempt(s): 719.35/297.04 ----------------------------- 719.35/297.04 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 719.35/297.04 failed due to the following reason: 719.35/297.04 719.35/297.04 match-boundness of the problem could not be verified. 719.35/297.04 719.35/297.04 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 719.35/297.04 failed due to the following reason: 719.35/297.04 719.35/297.04 match-boundness of the problem could not be verified. 719.35/297.04 719.35/297.04 719.35/297.04 719.35/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 719.35/297.04 the following reason: 719.35/297.04 719.35/297.04 We add the following weak dependency pairs: 719.35/297.04 719.35/297.04 Strict DPs: 719.35/297.04 { app^#(x, y) -> 719.35/297.04 c_1(helpa^#(0(), plus(length(x), length(y)), x, y)) 719.35/297.04 , helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs)) 719.35/297.04 , if^#(true(), c, l, ys, zs) -> c_7() 719.35/297.04 , if^#(false(), c, l, ys, zs) -> 719.35/297.04 c_8(helpb^#(c, l, greater(ys, zs), smaller(ys, zs))) 719.35/297.04 , plus^#(x, 0()) -> c_3(x) 719.35/297.04 , plus^#(x, s(y)) -> c_4(plus^#(x, y)) 719.35/297.04 , length^#(nil()) -> c_5() 719.35/297.04 , length^#(cons(x, y)) -> c_6(length^#(y)) 719.35/297.04 , helpb^#(c, l, cons(y, ys), zs) -> 719.35/297.04 c_12(y, helpa^#(s(c), l, ys, zs)) 719.35/297.04 , ge^#(x, 0()) -> c_9() 719.35/297.04 , ge^#(0(), s(x)) -> c_10() 719.35/297.04 , ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) 719.35/297.04 , greater^#(ys, zs) -> 719.35/297.04 c_13(helpc^#(ge(length(ys), length(zs)), ys, zs)) 719.35/297.04 , helpc^#(true(), ys, zs) -> c_15(ys) 719.35/297.04 , helpc^#(false(), ys, zs) -> c_16(zs) 719.35/297.04 , smaller^#(ys, zs) -> 719.35/297.04 c_14(helpc^#(ge(length(ys), length(zs)), zs, ys)) } 719.35/297.04 719.35/297.04 and mark the set of starting terms. 719.35/297.04 719.35/297.04 We are left with following problem, upon which TcT provides the 719.35/297.04 certificate MAYBE. 719.35/297.04 719.35/297.04 Strict DPs: 719.35/297.04 { app^#(x, y) -> 719.35/297.04 c_1(helpa^#(0(), plus(length(x), length(y)), x, y)) 719.35/297.04 , helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs)) 719.35/297.04 , if^#(true(), c, l, ys, zs) -> c_7() 719.35/297.04 , if^#(false(), c, l, ys, zs) -> 719.35/297.04 c_8(helpb^#(c, l, greater(ys, zs), smaller(ys, zs))) 719.35/297.04 , plus^#(x, 0()) -> c_3(x) 719.35/297.04 , plus^#(x, s(y)) -> c_4(plus^#(x, y)) 719.35/297.04 , length^#(nil()) -> c_5() 719.35/297.04 , length^#(cons(x, y)) -> c_6(length^#(y)) 719.35/297.04 , helpb^#(c, l, cons(y, ys), zs) -> 719.35/297.04 c_12(y, helpa^#(s(c), l, ys, zs)) 719.35/297.04 , ge^#(x, 0()) -> c_9() 719.35/297.04 , ge^#(0(), s(x)) -> c_10() 719.35/297.04 , ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) 719.35/297.04 , greater^#(ys, zs) -> 719.35/297.04 c_13(helpc^#(ge(length(ys), length(zs)), ys, zs)) 719.35/297.04 , helpc^#(true(), ys, zs) -> c_15(ys) 719.35/297.04 , helpc^#(false(), ys, zs) -> c_16(zs) 719.35/297.04 , smaller^#(ys, zs) -> 719.35/297.04 c_14(helpc^#(ge(length(ys), length(zs)), zs, ys)) } 719.35/297.04 Strict Trs: 719.35/297.04 { app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y) 719.35/297.04 , helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 719.35/297.04 , plus(x, 0()) -> x 719.35/297.04 , plus(x, s(y)) -> s(plus(x, y)) 719.35/297.04 , length(nil()) -> 0() 719.35/297.04 , length(cons(x, y)) -> s(length(y)) 719.35/297.04 , if(true(), c, l, ys, zs) -> nil() 719.35/297.04 , if(false(), c, l, ys, zs) -> 719.35/297.04 helpb(c, l, greater(ys, zs), smaller(ys, zs)) 719.35/297.04 , ge(x, 0()) -> true() 719.35/297.04 , ge(0(), s(x)) -> false() 719.35/297.04 , ge(s(x), s(y)) -> ge(x, y) 719.35/297.04 , helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 719.35/297.04 , greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 719.35/297.04 , smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 719.35/297.04 , helpc(true(), ys, zs) -> ys 719.35/297.04 , helpc(false(), ys, zs) -> zs } 719.35/297.04 Obligation: 719.35/297.04 runtime complexity 719.35/297.04 Answer: 719.35/297.04 MAYBE 719.35/297.04 719.35/297.04 We estimate the number of application of {3,7,10,11} by 719.35/297.04 applications of Pre({3,7,10,11}) = {2,5,8,9,12,14,15}. Here rules 719.35/297.04 are labeled as follows: 719.35/297.04 719.35/297.04 DPs: 719.35/297.04 { 1: app^#(x, y) -> 719.35/297.04 c_1(helpa^#(0(), plus(length(x), length(y)), x, y)) 719.35/297.04 , 2: helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs)) 719.35/297.04 , 3: if^#(true(), c, l, ys, zs) -> c_7() 719.35/297.04 , 4: if^#(false(), c, l, ys, zs) -> 719.35/297.04 c_8(helpb^#(c, l, greater(ys, zs), smaller(ys, zs))) 719.35/297.04 , 5: plus^#(x, 0()) -> c_3(x) 719.35/297.04 , 6: plus^#(x, s(y)) -> c_4(plus^#(x, y)) 719.35/297.04 , 7: length^#(nil()) -> c_5() 719.35/297.04 , 8: length^#(cons(x, y)) -> c_6(length^#(y)) 719.35/297.04 , 9: helpb^#(c, l, cons(y, ys), zs) -> 719.35/297.04 c_12(y, helpa^#(s(c), l, ys, zs)) 719.35/297.04 , 10: ge^#(x, 0()) -> c_9() 719.35/297.04 , 11: ge^#(0(), s(x)) -> c_10() 719.35/297.04 , 12: ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) 719.35/297.04 , 13: greater^#(ys, zs) -> 719.35/297.04 c_13(helpc^#(ge(length(ys), length(zs)), ys, zs)) 719.35/297.04 , 14: helpc^#(true(), ys, zs) -> c_15(ys) 719.35/297.04 , 15: helpc^#(false(), ys, zs) -> c_16(zs) 719.35/297.04 , 16: smaller^#(ys, zs) -> 719.35/297.04 c_14(helpc^#(ge(length(ys), length(zs)), zs, ys)) } 719.35/297.04 719.35/297.04 We are left with following problem, upon which TcT provides the 719.35/297.04 certificate MAYBE. 719.35/297.04 719.35/297.04 Strict DPs: 719.35/297.04 { app^#(x, y) -> 719.35/297.04 c_1(helpa^#(0(), plus(length(x), length(y)), x, y)) 719.35/297.04 , helpa^#(c, l, ys, zs) -> c_2(if^#(ge(c, l), c, l, ys, zs)) 719.35/297.04 , if^#(false(), c, l, ys, zs) -> 719.35/297.04 c_8(helpb^#(c, l, greater(ys, zs), smaller(ys, zs))) 719.35/297.04 , plus^#(x, 0()) -> c_3(x) 719.35/297.04 , plus^#(x, s(y)) -> c_4(plus^#(x, y)) 719.35/297.04 , length^#(cons(x, y)) -> c_6(length^#(y)) 719.35/297.04 , helpb^#(c, l, cons(y, ys), zs) -> 719.35/297.04 c_12(y, helpa^#(s(c), l, ys, zs)) 719.35/297.04 , ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) 719.35/297.04 , greater^#(ys, zs) -> 719.35/297.04 c_13(helpc^#(ge(length(ys), length(zs)), ys, zs)) 719.35/297.04 , helpc^#(true(), ys, zs) -> c_15(ys) 719.35/297.04 , helpc^#(false(), ys, zs) -> c_16(zs) 719.35/297.04 , smaller^#(ys, zs) -> 719.35/297.04 c_14(helpc^#(ge(length(ys), length(zs)), zs, ys)) } 719.35/297.04 Strict Trs: 719.35/297.04 { app(x, y) -> helpa(0(), plus(length(x), length(y)), x, y) 719.35/297.04 , helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) 719.35/297.04 , plus(x, 0()) -> x 719.35/297.04 , plus(x, s(y)) -> s(plus(x, y)) 719.35/297.04 , length(nil()) -> 0() 719.35/297.04 , length(cons(x, y)) -> s(length(y)) 719.35/297.04 , if(true(), c, l, ys, zs) -> nil() 719.35/297.04 , if(false(), c, l, ys, zs) -> 719.35/297.04 helpb(c, l, greater(ys, zs), smaller(ys, zs)) 719.35/297.04 , ge(x, 0()) -> true() 719.35/297.04 , ge(0(), s(x)) -> false() 719.35/297.04 , ge(s(x), s(y)) -> ge(x, y) 719.35/297.04 , helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) 719.35/297.04 , greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) 719.35/297.04 , smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) 719.35/297.04 , helpc(true(), ys, zs) -> ys 719.35/297.04 , helpc(false(), ys, zs) -> zs } 719.35/297.04 Weak DPs: 719.35/297.04 { if^#(true(), c, l, ys, zs) -> c_7() 719.35/297.04 , length^#(nil()) -> c_5() 719.35/297.04 , ge^#(x, 0()) -> c_9() 719.35/297.04 , ge^#(0(), s(x)) -> c_10() } 719.35/297.04 Obligation: 719.35/297.04 runtime complexity 719.35/297.04 Answer: 719.35/297.04 MAYBE 719.35/297.04 719.35/297.04 Empty strict component of the problem is NOT empty. 719.35/297.04 719.35/297.04 719.35/297.04 Arrrr.. 719.66/297.32 EOF